The CMS experiment uses self-triggering arrays of drift tubes in the barrel muon trigger to perform the identification of the correct bunch crossing. The identification is unique only if the trigger chain is correctly synchronized. In this paper, the synchronization performed during an extended cosmic ray run is described and the results are reported. The random arrival time of cosmic ray muons allowed several synchronization aspects to be studied and a simple method for the fine synchronization of the Drift Tube Local Trigger at LHC to be developed.
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